STRUCTURE OF GALLIUM ISOTOPES
By Prof. Lefteris Kaliambos (Λευτέρης Καλιαμπός)T.E. Institute of Larissa Greece. ( September 2014) Unfortunately the discovery of the assumed uncharged neutron (1932) along with the invalid relativity (1905) led to the abandonment of the well-established electromagnetic laws, in favor of various contradicting nuclear theories which cannot lead to the nuclear structure. Under this physics crisis in 2003 I published my paper “Nuclear structure is governed by the fundamental laws of electromagnetism ” by reviving the natural laws which led to my discovery of 288 quarks in nucleons including 9 charged quarks in proton and 12 ones in neutron able to give the nuclear binding and nuclear structure by applying the laws of electromagnetism (See my papers of nuclear structure in FUNDAMENTAL PHYSICS CONCEPTS ). Natural gallium (Ga) consists of a mixture of two stable isotopes: gallium-69 and gallium-71. The most commercially important radioisotopes are gallium-67 and gallium-68. Gallium-67 (half-life 3.3 days) is a gamma-emitting isotope (the gamma emitted immediately after electron-capture) which is used in standard nuclear medical imaging, in procedures usually referred to as gallium scans. It is usually used as the free ion, Ga3+. It is the longest-lived radioisotope of gallium. The shorter-lived gallium-68 (half-life 68 minutes) is a positron-emitting isotope which is generated from germanium-68 in gallium-68 generators, for use in a small minority of diagnostic PET scans. For this use, it is usually attached as a tracer to a carrier molecule, which gives the resulting radiopharmaceutical a different tissue-uptake specificity from the ionic Ga-67 radioisotope normally used in standard gallium scans. ' ' STRUCTURE OF Ga-61, Ga-63, Ga-65, Ga-67, Ga-69 AND Ga-71 WITH S = -3/2 For understanding the structure of the above nuclides having S = -3/2 you may study carefully the diagram of Ga-65 of my STRUCTURE OF Ga-65, Ga-67, Ga-69 AND Ga-71 . In the diagram of Ga-65 you see that the structure of the above nuclides belongs to a group which gives stable nuclides based on the structure of Ga-61 with S=-3/2, while the group with S=0 based on the structure of Ga-62 with S = 0 having 31protons and 31 neutrons gives always unstable nuclides because in such structures of S = 0 the p29 makes only two bonds per proton. In the diagram of Ga-65 we see that in the absence of four extra neutrons of opposite spins we get the structure of Ga-63 having the p29n29 with S =-1 and the one extra n32(-1/2) existing in front of p11. In such a structure the p29 makes 3 bonds per proton and the two bonds per neutron of the extra n32 are able to increase the binding energies of pn bonds. Then adding two neutrons of opposite spins or four neutrons we get the structures of the unstable Ga-63 and Ga-65 . In these cases we observe 2 or 4 blank positions for receiving extra neutrons with two bonds per neutron, but they cannot give enough energies to pn bonds for overcoming the pp and nn repulsions. Whereas the 6 and 8 blank positions of the stable Ga-69 and Ga-71 receive extra neutrons with two bonds per neutron able to give enough binding energies to pn bonds for overcoming the nn and pp repulsions However in heavier nuclides in the absence of blank positions as in the case of Ga-73 the two more extra neutrons than those of Ga-71 make single bonds leading to the decay. ' ' NUCLEAR STRUCTURE OF Ga-75, Ca-77, Ga-79, Ga-83, AND Ga-85 WITH S = -3/2 The structure of the above unstable nuclides is based on the structure of Ga-73 with S = -3/2. For example the Ga-85 with S =-3/2 has 12 more extra neutrons of opposite spins than those of Ga-73 which make single bonds leading to the decay. ' ' NUCLEAR STRUCTURE OF Ga- 59, AND Ga-57 WITH S = -3/2 In the absence of neutrons we see that the structure of the above unstable nuclides is based on the structure of Ga-63 with S = -3/2. For example in the Ga-57 with S = -3/2 we have 4 absent neutrons with opposite spins. ' ' NUCLEAR STRUCTURE OF Ga-62, Ga-64, AND Ga-66 WITH S =0 Here the Ga-62 with 31 protons and 31 neutrons has S = 0 because in the absence of the one extra n32(-1/2) the p29 changes the spin from -1/2 to +1/2. Particularly it goes from the sixth horizontal plane of negative spins to the first horizontal plane of positive spins. Since this change of spin of p29 gives S = +1 we see that in the absence of n32 (-1/2) the total spin of Ga-62 is given by S = -3/2 + 1 - 1(-1/2) = 0 Then we see that the structures of Ga-64 and Ga-66 are based on the structure of Ga-62 with S=0. For example in the presence of 4 extra neutrons of opposite spins we get the structure of Ga-66 with S = 0. ' ' NUCLEAR STRUCTURE OF Ga-68, Ga-70, Ga-72, Ga-74, Ga-76, Ga-78, Ga-80, Ga-82, Ga-84, AND Ga-86 After a careful analysis I found that the structure of the above unstable nuclides is based on the structure of Ga-62 with S = 0. For example the Ga-72 with S = -3 has 6 extra neutrons of negative spins and 4 extra neutrons of opposite spins. Whereas the Ga-80 with S = +3 has 6 extra neutrons of positive spins and 12 extra neutrons of opposite spins. NUCLEAR STRUCTURE OF Ga-60, Ga-58 AND Ga-56 In the absence of neutrons we conclude that the unstable structure of the above nuclides is based on a new structure which is similar to the structure of Ga-62. In this case the spin of Ga-62 is not S = 0 but S = +2. In the absence of extra neutrons looking again at the diagram of the Ga-65 we observe that the spin S=0 turns to the spin S =+2 when the p30n30 goes from the sixth horizontal plane of negative spins to the first horizontal plane of positive spins in order to make horizontal bonds with p1 and n1 in front of p1n1. Note that this movement gives S =+2 because the p30n30 changes the spin from S = -1 to S = +1. Under these new arrangements of nucleons in the structure of Ga-60 with S =+2 we have two absent neutrons of opposite spins. Whereas in the Ga-56 with S = +3 we have 2 absent neutrons of negative spins and 4 absent neutrons of opposite spins giving S = 0 . That is S = +2 - 2(-1/2) - 0 = +3